Fear vs. Worry: Are they the same?

My question today is: Is fear different than worry?
I feel like I have the worry thing down. I am able to cast aside my worries and freely give them to God. Occasionally, I think of something I might have forgot to do or tell someone and for that moment, I worry about the consequence or the reaction I will receive. But I am able to put the worry of the problem itself aside, pray about it and let it go. but fear, that's a whole other emotion for me. It's where I am stuck. I am afraid. Not afraid to live my every day life, not afraid to do things with my family or afraid to take chances, but I have fear. It's almost a surreal feeling to me because I can mentally tell myself that I am am afraid, that I shouldn't be afraid and I should stop being afraid, but my heart is still fearful.
and of what? what am I afraid of? a few things I can think of are spiders, heights, loss, rejection. these things, both external and internal are real heart punding, breath catching, adrenaline rushing things that cause my body to sweat, my heart to pound, my muscles to tense and my throat to burn. But why? Why do I have fear when fear should be as easy to give to God as worry. I have always found comfort in the verse Philippians 4:6-7.

Don't fret or worry. Instead of worrying, pray. Let petitions and praises shape your worries into prayers, letting God know your concerns. Before you know it, a sense of God's wholeness, everything coming together for good, will come and settle you down. It's wonderful what happens when Christ displaces worry at the center of your life.

I am so comforted by the fact that it is the wholeness of God that comes over me and calms me. That I don't need to worry because my prayers to Jesus takes the place of me having to worry. By knowing this and believing this, I think is the reason that I don't worry. I know I am taken care of and everything that happens in my life is coming together for good. (even when I don't see the good, I know it is part of His plan).
So now I ask, is fear just another extension of worry? Can it be given to God in prayer and removed from my life as a burden? Or is it something else that is different and needs to be dealt with in another way?
I'm not sure, but I want to find out and face my fears head on. I'll let you know what I find out as I go...